منابع مشابه
Kulikov’s problem on universal torsion-free abelian groups revisited
Let T be a torsion abelian group. We consider the class of all torsion-free abelian groups G satisfying Ext(G,T ) = 0 and search for λ-universal objects in this class. We show that for certain T there is no ω-universal group. However, for uncountable cardinals λ there is always a λ-universal group if we assume (V = L). Together with results by the second author this solves completely a problem ...
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We will answer a question raised by Emmanuel Dror Farjoun concerning the existence of torsion-free abelian groups G such that for any ordered pair of pure elements there is a unique automorphism mapping the first element onto the second one. We will show the existence of such a group of cardinality λ for any successor cardinal λ = μ+ with μ = μ0.
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We show, for each computable ordinal α and degree a > 0(α), the existence of a torsion-free abelian group with proper αth jump degree a.
متن کاملDegrees of orders on torsion-free Abelian groups
We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every (Turing) degree.
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It is known that many of the classes of simple Lie algebras of prime characteristic of nonclassical type have simple infinite-dimensional analogues of characteristic zero (see, for example, [4, p. 518]). We consider here analogues of those algebras which are defined by a modification of the definition of a group algebra. Thus we consider analogues of the Zassenhaus algebras as generalized by Al...
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ژورنال
عنوان ژورنال: Rendiconti del Seminario Matematico della Università di Padova
سال: 2020
ISSN: 0041-8994
DOI: 10.4171/rsmup/67